A professor whose Skype interview with the BBC went viral when his two young children invaded his office has admitted the video must have looked hilarious but he was mortified about it all the same.

Professor Robert Kelly was being interviewed live by the BBC's James Menendez when first his four-year-old daughter Marion skipped in, followed by his nine-month-old son James in a baby stroller. Finally his wife came in and tried to drag the children from the room as they loudly expressed their displeasure. They could be heard but not seen long after the door closed.

The video went viral on YouTube, was shared 84 million times on the BBC Facebook page, and was also trending on Twitter under the hashtag #BBCDAD. However Kelly - an expert in South Korean affairs who had been invited to discuss the impeachment of the country's President - admits he thought it might mean the end of his working relationship with the corporation.

"We were worried actually that the BBC would never call us again," US-born Kelly told Menendez in a second interview - this time with his wife and children at his side. "That was our first response – mortification that we had completely blown our relationship with you."

Kelly, who blames his family's newfound celebrity on forgetting to lock the office door, says he and his wife switched off their phones and social media off for several days following the interview.

Kelly, who is an associate professor in political science at Pusan National University, says he understands why the video was so popular but felt "pretty uncomfortable" that many viewers assumed wife Jung-a Kim was a maid or nanny. He met the former yoga teacher after moving to Busan in 2008.

Jung-a Kim herself was less bothered. "I hope people just enjoy it and don't argue over this thing," she said. "I'm not the nanny – that's the truth – so I hope they stop arguing."

Kelly was able to dispel another myth: that the reason he had not got up to remove his children was because he was wearing pyjama bottoms along with his shirt and tie. Kelly confessed that he was actually wearing jeans.

professor robert kelly BBC interview
Professor Kelly was being interviewed live by the BBC's James Menendez when his children stole the show BBC